Question

If a and b are the roots of the equation x2 - 6x + 6=0, then the value of a2 + b2 is

• A. 36
• B. 24
• C. 12
• D. 6

Answer 1

Answer: (B)

24

Answer 2

We have given the equation, $x^2 - 6x +6 = 0$

So, the Sum of roots = $a + b = 6$ – (i)

Product of roots = $ab = 6$

Squaring both sides in equation (i)

$(a + b)^2 = (6)^2$

$a^2 + b^2 + 2ab = 36$

$(a^2 + b^2) + 2(6) = 36$ as product of $ab = 36$

$(a^2 + b^2) = 36 - 12 = 24$

So, $(a^2 + b^2) = 24$

The correct option is (B): 24